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Friday, May 25, 2007

Riemann Revisited II

I'm so excited by this claim of Tribikram Pati! I haven't read the paper yet, but quoting from the abstract: our analysis shows that the assumption of the truth of the Riemann Hypothesis leads to a contradiction. Maybe he's right! After all, we've seen that the zeta function really shouldn't be studied within the confines of Boolean logic. But then there is already a post by Julia Kuznetsova claiming to have found the (almost inevitably present) flaw. A reply by a K. L. Lange to this criticism, supporting the proof, states, "So the main idea of [Pati] was to show, that we need that delta to prove RH, but there is no delta, so we cannot prove RH after all ..." In other words, the paper may well show that there is no proof of the Hypothesis within standard analysis. That doesn't sound surprising at all.

If we built an L function on the surreals in the M Theory operadic landscape, would we care about the ordinary Riemann zeta function? Yes, of course we would, because it's very interesting! And the M Theory L function would contain the Riemann one anyway. I have reluctantly come to the conclusion that a decent definition for n-logoses really must sort out the meaning of Analysis in category theory. This can't be done the 1-topos way. At least surreals have infinitesimals. And now I should probably confess that I always had great difficulties with analysis. Well, I also have great difficulties with Geometry, Algebra and Logic, which is one good reason for studying category theory, because it rolls them all into one! But as Donaldson, Perelman and many other mathematicians have shown, beautiful proofs these days need analysis.

Hi guys! Actually, the Pati paper business is a joke. If someone could show that RH is undecidable in the usual axioms, then RH would be true, not false, because if one can't decide it's false, then one can't find a zero off the critical line! But yes, however the RH turns out, it is fascinating for physics. Now, I must get back to that undecidability question....